Lippmann-Schwinger theory for two-dimensional plasmon scattering
Abstract
Long-lived and ultra-confined plasmons in two-dimensional (2D) electron systems may provide a sub-wavelength diagnostic tool to investigate localized dielectric, electromagnetic, and pseudo-electromagnetic perturbations. In this Article, we present a general theoretical framework to study the scattering of 2D plasmons against such perturbations in the non-retarded limit. We discuss both parabolic-band and massless Dirac fermion 2D electron systems. Our theory starts from a Lippmann-Schwinger equation for the screened potential in an inhomogeneous 2D electron system and utilizes as inputs analytical long-wavelength expressions for the density-density response function, going beyond the local approximation. We present illustrative results for the scattering of 2D plasmons against a point-like charged impurity and a one-dimensional electrostatic barrier due to a line of charges. Exact numerical results obtained from the solution of the Lippmann-Schwinger equation are compared with approximate results based on the Born and eikonal approximations. The importance of nonlocal effects is finally emphasized.
Cite
@article{arxiv.1702.04925,
title = {Lippmann-Schwinger theory for two-dimensional plasmon scattering},
author = {Iacopo Torre and Mikhail I. Katsnelson and Alberto Diaspro and Vittorio Pellegrini and Marco Polini},
journal= {arXiv preprint arXiv:1702.04925},
year = {2017}
}
Comments
23 pages, 8 multi-panel figures